1 Data Preparation

Before describing the data, we conducted some initial checks to ensure that all observations were entered within their possible ranges (for continuous variables) or levels (for categorical variables). We used some initial visualisations of the marginal distributions and relationships amongst the variables to find these impossible values (see Figure 5.1 for these for the pre-processed data in the Appendix). We excluded impossible values along with any observation containing missing data (Nexcluded = 5). Table 5.1 in the Appendix provides an overview of these excluded data points and the reason for exclusion. Additionally, the spelling of ‘Apple’ was corrected in the operating system entry of 7 observations from ‘Appple’.

2 Data Description

2.1 Association Between Operating System and Frequency of Emoji Use

We explored whether there’s a difference in the frequency of emoji use between Apple and Android users. We did this in two ways - we created violin plots, and conducted a Welch two sample t-test.

From Figure 2.1, we can see that the lower quartile and median of the two operating systems are very similar. However, the upper quartile is higher and overall range is larger for Apple than Android. It seems that Apple users seem more likely to use a higher number of emojis per day. Android users, however, are more densely concentrated around the median. There are only three unusually high values at 24 emojis per day, which are all reported by Apple users.

Frequency of Emoji Use on Apple and Android Operating System

Figure 2.1: Frequency of Emoji Use on Apple and Android Operating System

Following this, we conducted a Welch two sample t-test to assess whether the mean frequency of emoji use was different between Android (n = 109 ; m = 4.3; sd = 3.77 and Apple users (n = 126; m = 5.87; sd = 6.01). There was a significant difference in emoji use among Android and Apple users, t(213.42) = -2.39, p = 0.018, two-tailed).Therefore, we reject the null hypothesis that there is no difference in emoji use between Apple and Android users. From these two mechanisms, we have concluded that there is a difference between the two operating systems.

2.2 Correlation Between Age and Frequency of Emoji Use

In order to assess whether there is a relationship between the age of an individual, and the frequency by which they use emoji we were going to conduct a Pearson correlation test. Figure 2.2 visually illustrates a clear negative correlation between Age and the Frequency of Emoji Use. The accompanying histogram on the side of the plot reveals that the frequency of emoji use follows the Poisson distribution. Additionally, the histogram positioned above the scatterplot demonstrates that age is uniformly distributed. Importantly, figure 2.2 clarifies that age and the frequency of emoji use do not exhibit a linear relationship. These facts are also verified by a Shapiro–Wilk test (w (frequency of emoji use) = 0.85, p < 0.001, w (age) = 0.94, p < 0.001). Since both a normal distribution and a linear relationship are assumptions of a Pearson correlation test, we decided to conduct a Spearman’s rank correlation test, which assumes neither normality nor a linear relationship.

Relationship Between Age and Frequency of Emoji Use

Figure 2.2: Relationship Between Age and Frequency of Emoji Use

The Spearman’s rank correlation test was conducted to assess whether there is a relationship between the age of an individual, and the frequency by which they use emoji. A total of 237 individuals were included in the analysis, with a mean age of 35.39 (sd = 13.4) and a mean frequency of use of emoji of 5.16 (sd = 5.13).There was a strong negative correlation between age of an individual and the frequency of emoji use (R = -0.86, S = 4.1289235^{6}), p < < 0.001. We therefore reject the null hypothesis that there is no correlation between age and frequency of emoji use.

2.3 Balance of Users of Operating Systems for Emoji Categories

Distribution of Participants on Apple and Android Operating System for Each Emoji Category

Figure 2.3: Distribution of Participants on Apple and Android Operating System for Each Emoji Category

Finally, we investigated whether there is a balance between Apple and Android users for each category of emoji. Figure 2.3 shows the distribution of operating systems for each emoji category. For all categories we can see that the number of Apple users is slightly larger than Android users, with the largest difference being in the Thumbs up category. We conducted a \(\chi^2\) goodness of fit test for each emoji category to test if these differences were significant. This tested if the observed proportion of participants using each operating system deviated from a hypothesised equal proportion of users (50% of the data each), which would indicate balance.

For each emoji category, we found no significant difference between the observed proportions of Apple and Android users, and a hypothesised set of equal proportions. For loudly crying face emoji [😭], \(\chi^2\) (1) = 0.05, p = 0.831 (n = 88, proportionApple = 51.14 %). For the slightly smiling face emoji [🙂], \(\chi^2\) (1) = 0.22, p = 0.637 (n = 72, proportionApple = 52.78 %). Finally, for the thumbs up Emoji [👍], \(\chi^2\) (1) = 1.61, p = 0.204 (n = 75, proportionApple = 57.33 %). Thus, we found no evidence of imbalance of users of Apple and Android operated phones in each emoji category.

3 The Emotional Effect of Emojis

To do * maybe have a little section on this ” this is the question” lets look at the plots * plot commentary

One of the main aims we address in this research is the investigation of factors influencing emotional valence. We fitted a multiple regression model to predict whether the frequency of use of the emoji, the type of emoji, as well as the age of the participants, and the interaction between age and emoji category has an effect on their emotional valence. We mean-centered age and scaled the emotional valence score for interpretation of coefficients and intercepts. Emoji category was treatment coded with the “loudly crying face [😭]” as the reference level.

As noted previously, neither age (approximately uniform; Figure 3.1D) nor frequency of Emoji use (approximately Poisson distributed; Figure 3.1E) were normally distributed. There were slightly more participants in the loudly crying face emoji [😭] than the other emoji categories (Figure 3.1). Figure 3.1 B also indicates a negative relationship between age and emotional valence score; as age increases, the emotional valence score decreases. In particular, the loudly crying face emoji [😭] shows a steep negative correlation with age. These relationships will be more closely evaluated in our linear regression model.

## Non-constant Variance Score Test 
## Variance formula: ~ fitted.values 
## Chisquare = 12.86873, Df = 1, p = 0.00033412
Relationships (A-B) and Marginal Distributions (C-F) of Variables of Interest for Emotional Effect

Figure 3.1: Relationships (A-B) and Marginal Distributions (C-F) of Variables of Interest for Emotional Effect

Prior to conducting our analyses, we assessed whether the assumptions for conducting a linear model were met. Model residuals seemed normally distributed ??. Despite a significant Shapiro-Wilks (W = 0.91, p < 0.001, this was not particularly problematic due to the large sample size of the study (237). Visual inspection of Scale Location (ncvTest_int) showed a straight line, but datapoints were not evenly spread out. Furthermore, the Breusch-Pagan test was significant (\(\chi^2\) (1) = 12.87, p < 0.001, which might also not be a problem due to… Given the previously found strong correlation between age and frequency of emoji use, we checked for multicollinarity between the variables. Multicollinarity did not seem to be a problem, as all GVIF were <5 ??. We furthermore conducted a Cooks Distance analysis and identified three outliers ??. The threshold for this determination was given by \(4/(N-k-1)\), in which N is the number of observations and k is the number of predictors. Given this threshold of 0.017, it was determined that we should exclude three observations and fit a new model without them.

Table 3.1: Emotional Effect of Emojis: Analysis of Variance Table (Sensitivity Analysis)
Df Sum of Squares Mean Sum of Squares F value P value
Emoji usage 1 93.84 93.84 172.89 < 0.001
Age 1 0.66 0.66 1.22 0.271
Emoji category 2 1.97 0.98 1.81 0.166
Age:Emoji category 2 13.31 6.65 12.26 < 0.001
Residuals 227 123.22 0.54
Table 3.2: Linear Regression Model
  Emotional Valence (Full Dataset Model) Emotional Valence (Reduced Dataset Model
Predictors Estimates std. Error 95 % CI t-statistic p-value Estimates std. Error 95 % CI t-statistic p-value
Intercept -0.47 0.12 -0.71 – -0.23 -3.83 <0.001 -0.60 0.11 -0.81 – -0.38 -5.46 <0.001
Emoji use frequency 0.08 0.02 0.04 – 0.11 4.57 <0.001 0.12 0.02 0.08 – 0.15 7.49 <0.001
Age -0.03 0.01 -0.04 – -0.01 -3.34 0.001 -0.03 0.01 -0.04 – -0.01 -3.73 <0.001
Emoji [🙂] 0.21 0.13 -0.04 – 0.47 1.63 0.105 0.11 0.12 -0.13 – 0.34 0.89 0.374
Emoji [👍] 0.00 0.13 -0.25 – 0.26 0.02 0.981 -0.10 0.12 -0.33 – 0.12 -0.89 0.372
Age:Emoji [🙂] 0.02 0.01 0.00 – 0.04 2.18 0.030 0.04 0.01 0.02 – 0.06 4.39 <0.001
Age:Emoji [👍] 0.02 0.01 -0.00 – 0.04 1.82 0.070 0.03 0.01 0.02 – 0.05 3.91 <0.001
Observations 237 234
R2 / R2 adjusted 0.340 / 0.323 0.471 / 0.457

An analysis of variance was conducted on the model that excluded the three outlying values. This analysis indicated that frequency of emoji use was a significant predictor of the emotional valence score (p<0.001), and the interaction between age and emoji category was also found to be a significant predictor (p<0.001). This model explained 46% (adjusted R2) of the variance within the data.

Prior to removing the three values that were shown to have undue influence on the model fit, we fit a model including all values present in the dataset. The two models are compared in 3.2. When the three influential values were removed, the interaction between all three categories of emoji and age reached significance (pslightly_smiling <0.001, pthumbs_up <0.001, ploudly_crying <0.001). These interactions are plotted in 3.2. Additionally, the refitted model explained 14% more of the variance in the data.

The interaction of Age and Emoji Category on the EVS

Figure 3.2: The interaction of Age and Emoji Category on the EVS

3.1 Conclusion

4 Accuracy of Emoji Interpretation (Julie)

To do

Finally, we address what factors make participants more or less likely to correctly interpret Emoji (according to the researchers’ coding scheme). The predictors of interest were the same as the previous regression model; frequency of emoji use first as its effect on interpreting Emoji is already known, and additionally age and Emoji category along with the interaction between these to investigate if there is an effect of age on interpretation accuracy and if this depends on the Emoji. Figure 4.1 provides an overview of the marginal distributions of these variables (Figures 4.1C-F) and the relationships with Emoji interpretation accuracy for age by Emoji category (Figure 4.1A) and for frequency of Emoji use (Figure 4.1B). Generally, a slightly higher proportion of participants interpreted their Emoji incorrectly as compared to correct interpretations (Figure 4.1F). Examining the median age and frequency in Figures 4.1A-B, it seems that incorrect responses are more common for participants with higher age and lower frequency use. Although correct responses were more evenly distributed across frequency of Emoji use relative to incorrect responses, which tended to be below five Emoji per day. Figure 4.1A provided some indication that the Emoji being interpreted may moderate the relationship between lower age for correct interpretations - specifically, that the thumbs up Emoji [👍] seem to have slightly lower median age for correct interpretations and seem to be generally harder to interpret correctly.

Relationships (A-B) and Marginal Distributions (C-F) of Variables of Interest for Interpretation Accuracy

Figure 4.1: Relationships (A-B) and Marginal Distributions (C-F) of Variables of Interest for Interpretation Accuracy

4.1 Model Fitting and Planned Analysis

Given the binary outcome (correct vs. incorrect interpretation; see Figure 4.1F), we fitted a multiple logistic regression model via maximum likelihood estimation. This estimates the change in log-odds for correct interpretation for each predictor (see eq. (4.1)). We included the predictors as outlined above. Like the previous model, we mean-centered age so that the log-odds of the intercept are estimated at the mean age of the sample rather than extrapolated to age 0. Secondly, we used zero-to-sum coding (coding scheme in the Appendix, Table 5.2) for the Emoji category since there was no intuitive reference group. The two regression coefficients for Emoji category would be the difference between the mean log-odds of correct interpretation across Emoji categories and the Emoji-specific mean log-odds for the loudly crying face Emoji and the thumbs up Emoji. We specifically these levels due to the seemingly lower age but lower accuracy for correctly interpreting the thumbs up Emoji given the researchers’ interest in these categories interaction with age. Thus, we fitted a model where the intercept was the log-odds of correctly interpreting an Emoji averaged across the different categories for a mean-aged participant reporting using 0 Emoji per day. Equation (4.1) (note, E1 and E2 refers to the sum-to-zero coding in Table 5.2 in the Appendix):

\[\begin{align} \log[ \frac {P(Correct)}{P(Incorrect)}] = & \ \hat\beta_0 + \hat\beta_{1}(Frequency) + \hat\beta_{2}(Age) + \hat\beta_{3}D_{1[thumbs \ up]} + \hat\beta_{4}D_{2[loudly\ crying]} \ + \\ & \ \hat\beta_{5}(Age · E_{1[thumbs \ up]}) + \hat\beta_{6}(Age · E_{2[loudly\ crying]}) \tag{4.1} \end{align}\]

We conducted the following tests (all at \(\alpha\) = .05 unless otherwsie stated) to address which factors are associated with more or less likelihood of correctly interpreting the tested Emoji. Firstly, we tested which of the predictors and the interaction significantly an analysis of deviance was conducted using likelihood ratio (\(\chi^2\)) tests to test if each significantly reduced model deviance. Secondly, we examined each regression coefficient, its direction, range with 95 % confidence intervals, and significance with z-tests (\(H_0: \hat\beta_i \neq 0\)). We also estimated these for slightly smiling face Emoji category (\(\hat\beta_0-(\hat\beta_3+\hat\beta_4)\)) and its interaction with age (\(\hat\beta_0-(\hat\beta_5+\hat\beta_6)\)). Before examining the model, we verified that the model fit did not violate assumptions of logistic regression by inspecting the range of the standardised deviance residuals (plotted in Figure 5.3; a priori criterion range: \(|standardised \ deviance \ residual| ≤ 3\)). Given the sizable correlation between frequency of Emoji use and age (see Data Description), we also confirmed that multicollinearity, i.e., model estimates being influenced by correlated predictors, was negligible by estimating generalised variance inflation factors for each predictor (all below a priori criterion of 5; see Table ??). Finally,the Cook’s distances, i.e., the average change in predictors if removing each observation, indicated three potentially influential observations (see Appendix, Figure 5.4). After inspecting these (see Appendix, Table ??) and how they influenced model predictors (via DFBeta values; see Appendix, Table ??), we performed two sensitivity analyses excluding a variable strongly affecting the slope of age, and two variables affecting the slopes of Emoji category. Comparing these results to our original model fit and considering the interests of the researchers, we report the results for the full dataset. Yet, we comment briefly on the findings of the sensitivity analyses and provide their results in the Appendix.

4.2 Results

As shown in Table 4.1, likelihood ratio tests indicated that all predictors except Emoji category significantly reduced deviance residuals, thus, improving the model(ps < 0.001). The interaction between age and emoji category further reduced deviance of the model (\(\chi^2\)(2) = 7.12, p = 0.028). Thus, age and its interaction with Emoji category reduced model deviance beyond what could be accounted for by frequency of Emoji use.

Table 4.1: Emoji Interpretation: Analysis of Deviance Table
Df Deviance Residual Df Residual Deviance p-value
Intercept-only 236 324.49
Emoji use frequency 1 96.51 235 227.97 < 0.001
Age 1 24.04 234 203.94 < 0.001
Emoji category 2 1.91 232 202.03 0.385
Age:Emoji category 2 7.12 230 194.91 0.028

Looking at how these variables predicted accurate interpretation, we found that per year older, the odds of making an incorrect interpretation increased 1.08 times (odds ratio = 0.92, ). However, this was moderated by which Emoji was interpreted. The thumbs of Emoji enhanced the negative effect of age by increasing the odds of making an incorrect interpretation increased 1.02 times () relative to the effect of age across categories. Meanwhile, the loudly crying face Emoji slightly attenuated the decreased performance age by increasing the odds of correct interpretation by 0.98 times () compared to the effect of age across all Emojis tested. We found no significant association between correct interpretation log-odds and Emoji use frequency or any of the Emoji categories (although see the Sensitivity Analysis below for the latter). A full overview of regression results as odds ratios are reported in Table 4.2. Note, that this discrepancy of significant association for the frequency of Emoji use between the analysis of deviance and logistic regression may be related to how much it uniquely reduces model deviance and its correlation with age. Specifically, it may account for a large amount of deviance of which a substantial proportion is shared with age - thus, in the analysis of deviance due to its antecedency this overlap was attributed to it, yet, in the linear model only non-overlapping deviance is considered. This also suggests that age has a sizable amount of unique deviance compared to frequency.

Table 4.2: Logistic Regression Model
  Correct Emoji Interpretation
Predictors Odds Ratio std. Error 95 % CI z-statistic p-value
Intercept 0.52 0.21 0.24 – 1.12 -1.65 0.098
Emoji use frequency 1.12 0.08 0.99 – 1.29 1.68 0.092
Age 0.92 0.03 0.87 – 0.97 -2.83 0.005
Emoji [👍] 0.67 0.28 0.29 – 1.51 -0.97 0.333
Emoji [😭] 0.34 0.18 0.11 – 0.91 -2.02 0.044
Age:Emoji [👍] 0.98 0.04 0.91 – 1.05 -0.54 0.588
Age:Emoji [😭] 0.86 0.06 0.74 – 0.97 -2.20 0.028
Observations 237
Deviance 194.912
log-Likelihood -97.456
Predicted Probability of Correct Emoji Interpretation Age for Each Emoji Tested

Figure 4.2: Predicted Probability of Correct Emoji Interpretation Age for Each Emoji Tested

Due to the linear transformation of probability of correct interpretation into log-odds (see Equation (4.1)), the increase in probability of correctly interpreting an Emoji for a given predictor is not constant. Figure 4.2 visualises the predicted probability of correctly interpreting for the age by Emoji category interaction; the probability of accurately interpreting the Emoji for the sample age range, split by each Emoji category, and holding frequency of Emoji use constant (at 0). Emphasising what was found in the regression coefficients, the thumbs up Emoji appear to have a stronger association with age than other Emoji categories. Although as shown by the overlapping uncertainty ranges, the predicted effects may also be very similar for most ages.

4.3 Sensitivity Analyses

We conducted two sensitivity analyses of these results due to potential influence. Firstly, we found two influential values, which from their DFBetas indicated a strong influence on the Emoji category coefficients. Upon excluding these, both the loudly crying face Emoji and the thumbs up Emoji predicted significant chances We chose not to report these as main results because the researchers were not interested in the main effect of Emoji category (only its interaction with age).

Age exclusion We reported the more moderate results with this outlier included as the significance of age was unaffected and to not overly inflate the results for a variable of interest. These analyses do suggest that the association between correct interpretation and age may be slightly stronger than reported in the main analysis.

4.4 Conclusion

We found that higher age made participants less likely to interpret Emoji correctly although the extent of this was moderated by the Emoji being interpreted. Thumbs up Emoji had a stronger association while the loudly crying Emoji had a slightly weaker relationship with age and interpretation accuracy. Frequency of Emoji use

5 Appendix: Supplementary Tables and Figures

5.1 Data Preparation

Table 5.1: Excluded Observations
Name Age Operating system Emoji use frequency Emoji category Emotional valence score Emoji Interpretation Reason for exlcusion
Beatrix Potter 28 Apple 6 upside-down face -4.0211784 incorrect Emoji not in study materials is reported
Thomas Burnet 1 Android 6 slightly smiling face 13.1687730 incorrect Impossible or unlikely age
Joseph Priestley NA Apple 10 slightly smiling face -1.1653997 correct Age is missing
Robert Bunsen -99 Apple 6 thumbs up 0.4258727 incorrect Impossible or unlikely age
Luigi Galvani 43 Apple -4 slightly smiling face 3.7097433 incorrect Impossible frequency value (negative) is reported
Marginal Distributions and Between-Variable Relationships for Pre-Processed Data

Figure 5.1: Marginal Distributions and Between-Variable Relationships for Pre-Processed Data

5.2 Data Description

QQPlot

Figure 5.2: QQPlot

5.3 The Emotional Effect of Emojis

Table 5.2: Emoji Category Treatment Contrast Coding Scheme
E1 E2
Loudly crying face 0 0
Slightly smiling face 1 0
Thumbs up 0 1 

##                               GVIF Df GVIF^(1/(2*Df))
## freq_emu                  2.610305  1        1.615644
## I(age - mean(age))        3.893405  1        1.973171
## em_cat                    1.006897  2        1.001720
## I(age - mean(age)):em_cat 2.451011  2        1.251228
## Potentially influential observations of
##   lm(formula = scale(EVS) ~ freq_emu + I(age - mean(age)) * em_cat,      data = emoji_clean) :
## 
##     dfb.1_ dfb.frq_ dfb.I(-m dfb.e_sf dfb.e_Tu dfb.I-msf dfb.I-mu dffit  
## 2   -0.31  -0.13     0.58     0.38     0.38    -0.55     -0.54    -1.03_*
## 13   0.65  -0.93    -0.57     0.64     0.01    -0.89     -0.04     1.62_*
## 43  -0.05   0.07     0.05     0.19     0.00     0.30      0.00     0.50  
## 80   0.14  -0.19    -0.12     0.01    -0.06    -0.01      0.09    -0.25  
## 97   0.02  -0.02    -0.01     0.00    -0.01     0.00      0.01    -0.03  
## 153 -0.05   0.14     0.01    -0.05    -0.05     0.07      0.07     0.19  
## 175  0.39  -0.55    -0.34     0.02     0.46    -0.02     -0.84     1.36_*
## 206 -0.19   0.27     0.16    -0.01     0.08     0.01     -0.14     0.35  
##     cov.r   cook.d hat    
## 2    0.46_*  0.13   0.03  
## 13   0.41_*  0.33   0.07  
## 43   0.90_*  0.03   0.04  
## 80   1.14_*  0.01   0.11_*
## 97   1.16_*  0.00   0.11_*
## 153  1.10_*  0.00   0.08  
## 175  0.47_*  0.24   0.06  
## 206  1.13_*  0.02   0.11_*

5.4 Accuracy of Emoji Interpretation

Standardised Deviance Residuals for Logistic Regression Model

Figure 5.3: Standardised Deviance Residuals for Logistic Regression Model

GVIF Df
Emoji use frequency 2.05 1
Age 2.65 1
Emoji category 1.44 2
Age:Emoji category 2.42 2
Cook's Distances for Logistic Regression Model

Figure 5.4: Cook’s Distances for Logistic Regression Model 

##          dfb.1_    dfb.frq_    dfb.ag_m     dfb.e_sf    dfb.e_Tu     dfb.a_sf
## 13  -0.27149090  0.37077349  0.21963763 -0.182888348  0.02066670  0.397892363
## 75  -0.13153127  0.17963146  0.10640952 -0.012557631  0.42425728  0.014437092
## 218  0.02399911 -0.03277544 -0.01941541  0.002291257  0.33745009 -0.002634182
## 146  0.02430393 -0.03319173 -0.01966201  0.002320359 -0.05224189 -0.002667640
##       dfb.a_:u      dffit     cov.r     cook.d        hat
## 13  0.00197523 -0.6542230 1.0031819 0.06199454 0.09358556
## 75  0.44421545  0.5643422 0.8850323 0.09108583 0.04587707
## 218 0.37656364  0.4474885 0.8199488 0.09805434 0.02325003
## 146 0.30312461 -0.4437990 0.9521531 0.03013611 0.04526393
##               name age   opsys freq_emu                em_cat       EVS
## 13  Mary Ainsworth  16 Android        4 Slightly smiling face 36.970859
## 75      Max Planck  42 Windows        6             Thumbs up -6.172675
## 218   Robert Bosch  43   Apple        1             Thumbs up -2.323922
## 146 William Ramsay  25   Apple        7             Thumbs up  5.063527
##            EI em_cat_emoji EI_bi       age_mc
## 13  Incorrect           🙂     0 -19.3924....
## 75    Correct           👍     1 6.607594....
## 218   Correct           👍     1 7.607594....
## 146 Incorrect           👍     0 -10.3924....
Table 5.3: Emoji Interpretation: Analysis of Deviance Table (Sensitivity Analysis 1)
Df Deviance Res. Df Res. Deviance p-value
Intercept-only 234 321.13
Emoji usage 1 98.08 233 223.05 < 0.001
Age 1 25.76 232 197.29 < 0.001
Emoji category 2 2.96 230 194.34 0.228
Age:Emoji category 2 15.32 228 179.01 < 0.001
Table 5.3: Emoji Interpretation: Analysis of Deviance Table (Sensitivity Analysis 2)
Df Deviance Res. Df Res. Deviance p-value
Intercept-only 235 323.34
Emoji usage 1 96.28 234 227.06 < 0.001
Age 1 26.86 233 200.20 < 0.001
Emoji category 2 1.82 231 198.38 0.403
Age:Emoji category 2 7.02 229 191.36 0.03

Note. Res. stands for residual. Emoji usage refers to frequency of Emoji use.

Table 4.2: Table of Coefficients for the Reported Model and Sensitivity Analyses for Emoji Interpretation Accuracy
  Reported model Sensitivity Analysis 1 Sensitivity Analysis 2
Predictors Odds Ratio std. Error 95 % CI z-statistic p-value Odds Ratio std. Error 95 % CI z-statistic p-value Odds Ratio std. Error 95 % CI z-statistic p-value
Intercept 0.52 0.21 0.24 – 1.12 -1.65 0.098 0.56 0.22 0.25 – 1.21 -1.47 0.142 0.58 0.23 0.26 – 1.26 -1.36 0.174
Emoji use frequency 1.12 0.08 0.99 – 1.29 1.68 0.092 1.10 0.08 0.97 – 1.27 1.43 0.152 1.09 0.08 0.96 – 1.26 1.29 0.196
Age 0.92 0.03 0.87 – 0.97 -2.83 0.005 0.92 0.03 0.87 – 0.97 -2.91 0.004 0.92 0.03 0.86 – 0.97 -3.00 0.003
Emoji [👍] 0.67 0.28 0.29 – 1.51 -0.97 0.333 0.67 0.28 0.29 – 1.52 -0.95 0.340 0.72 0.31 0.31 – 1.66 -0.77 0.443
Emoji [😭] 0.34 0.18 0.11 – 0.91 -2.02 0.044 0.09 0.08 0.01 – 0.41 -2.61 0.009 0.34 0.18 0.11 – 0.90 -2.04 0.042
Age:Emoji [👍] 0.98 0.04 0.91 – 1.05 -0.54 0.588 0.98 0.04 0.91 – 1.05 -0.56 0.576 0.96 0.04 0.89 – 1.04 -0.91 0.365
Age:Emoji [😭] 0.86 0.06 0.74 – 0.97 -2.20 0.028 0.71 0.10 0.49 – 0.88 -2.46 0.014 0.86 0.06 0.74 – 0.97 -2.20 0.028
Observations 237 235 236
Deviance 194.912 179.015 191.364
log-Likelihood -97.456 -89.507 -95.682
Predicted Probability of Correct Emoji Interpretation Age for Each Emoji Tested for (A) Sensitivity Analysis 1 and (B) Sensitivity Analysis 2

Figure 5.5: Predicted Probability of Correct Emoji Interpretation Age for Each Emoji Tested for (A) Sensitivity Analysis 1 and (B) Sensitivity Analysis 2

6 Exam Numbers: “B155926, B239086, B239979, B244840, B246814”

7 Assumptions for Interaction model and Logistic Regression model

8 Notes for report (to be deleted)

(JMEP; 16/11/2023 - midnight zoomies) found this cool way of generating lm equation :0 equatiomatic

(JMEP; 16/11/2023 - midnight zoomies) Would be helpful if we could do all our code for each section in one chunk. Then we can call tables/figures where we need them and refer to numbers in inline code. Inline code example: NA (there is an NA in age, booo)

(JMEP; 16/11/2023 - midnight zoomies) I looked into age. There is one NA, one person who is -100 years old and one that is 1 year old. I think we can reliably remove them (done in emoji_clean). There are also a bunch (23 to be exact) that are under 18 (between 14 and 17), whom I am not sure if we should remove?? I also noticed some other unusual stuff. Frequency ratings below 0, and a typo in “Apple” for one of the operating systems (“Appple”). There are also only two Windows users which isn’t really helpful in terms of analysis - might wanna exclude them.

8.1 Code to possibly be deleted:

8.2 probably to delete but just in case

For each emoji category, we found no significant difference between the observed proportions of Apple and Android users, and a hypothesised set of equal proportions. The results for each emoji category are as follows: loudly crying face emoji [😭]: n = 88, proportionApple = 51.14 %, proportionAndroid = 48.86 %; \(\chi^2\) (1) = 0.05, p = 0.831; slightly smiling face emoji [🙂]: n = 72, proportionApple = 52.78 %, proportionAndroid = 47.22 %; \(\chi^2\) (1) = 0.22, p = 0.637; thumbs up emoji [👍]: n = 75, proportionApple = 57.33 %, proportionAndroid = 42.67 %; \(\chi^2\) (1) = 1.61, p = 0.204.

8.3 again probably to delete - includes android proportion

For each emoji category, we found no significant difference between the observed proportions of Apple and Android users, and a hypothesised set of equal proportions. For loudly crying face emoji [😭], \(\chi^2\) (1) = 0.05, p = 0.831 (n = 88, proportionApple = 51.14 %, proportionAndroid = 48.86 %). For the slightly smiling face emoji [🙂], \(\chi^2\) (1) = 0.22, p = 0.637 (n = 72, proportionApple = 52.78 %, proportionAndroid = 47.22 %). Finally, for the thumbs up Emoji [👍], \(\chi^2\) (1) = 1.61, p = 0.204 (n = 75, proportionApple = 57.33 %, proportionAndroid = 42.67 %). Thus, we found no evidence of imbalance of users of Apple and Android operated phones in each emoji category.